Whitman now leads Poizner 38 percent to 29 percent among Republicans who said they were likely to vote in the June 8 primary, the survey by the Public Policy Institute of California found.

Whitman had 61 percent support in the same poll taken in March compared to 11 percent for Poizner. Since then, Poizner has begun spending millions of dollars on television and radio advertising, much of it directed at Whitman and criticizing her position on illegal immigration, her ties to Goldman Sachs and her poor voting record.

Both candidates have funneled millions into the race. Whitman, a billionaire, has donated $68 million to her campaign from her personal fortune. Poizner, a multimillionaire technology entrepreneur, has given $24.4 million to his campaign.

Despite the heavy spending in the governor's race and increased attention on the U.S. Senate primary, about a third of likely GOP voters remain undecided. The two front-runners in the Republican contest to challenge Democratic U.S. Sen. Barbara Boxer in the fall remain in a statistical dead heat, the survey found.

Support for former Hewlett-Packard chief executive Carly Fiorina and former congressman Tom Campbell was virtually unchanged since March, with Fiorina leading 25 percent to 23 percent, within the poll's sampling error for GOP primary voters.

Many voters are turning to the right, helping state Assemblyman Chuck DeVore, a favorite of the tea party, gain 8 percentage points since March. He still trails Fiorina and Campbell with 16 percent support.

"It's a real signal of how unsettled the electorate is, that you've got three in 10 saying that they're undecided when so much money and resources and media attention has occurred in the last few months, starting much earlier than usual," said Mark Baldassare, president of the Public Policy Institute.